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The system a² x - a y = 1 - a and b x + (3 - 2b) y = 3 + a has the unique solution x = 1, y = 1. Then:

1. a = 1, b = -1
2. a = -1, b = 1
3. a = 0, b = 0
4. none

Correct answer: a = 1, b = -1

Solution

Substituting (1,1) gives a² = 1 and b = -a; only a = 1, b = -1 yields a nonzero determinant (unique solution), since a = -1, b = 1 makes the system determinant zero.

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